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Question #3 (20 points): The phone lines to a rental car company are occupied 30% of...
Problem 4: The phone lines to an airline reservation systenm are occupied 50% of the time....
Problem 4: The phone lines to an airline reservation systenm are occupied 50% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline. a) What is the probability that for exactly three calls the lines are occupied? not occupied? all occupied? b) What is the probability that for at least one call the lines are e) What is the expected number of calls in...
For Exercises 3-15 to 3-18, verify that the following functions are probability mass functions, and determine...
For Exercises 3-15 to 3-18, verify that the following functions are probability mass functions, and determine the requested probabilities. 3-15. x 2 x)1/8 2/8 2/8 2/8 18 (a) P(Xs 1) (c) P(-1 X (b) P(X-2) (d) P(X--1 1) or X= 2) 3-28. The data from 250 endothermic reactions involving sodium bicarbonate are summarized as follow Final Temperature Conditions 266 K 271 K 274 K Number of Reactions 70 80 100 33. Determine the cumulative distribution function for the random variable...
random probability course Problem 1: [60 points) A discrete random variable has the following probability mass...
random probability course
Problem 1: [60 points) A discrete random variable has the following probability mass function 2s+ 1,2,3 Find: (a) P(x <2) (b) P(l s X<3) (c) E(x) (d) Ea/x) Problem 2: [40 points] Calls to an airline reservation system have a probability of 0.7 of connecting successfully (i.e., not obtaining a busy tone). Assume that 8 independent calls are placed to the airline. (a) What is the probability that at least one call will connect successfully? (b) What...
A real estate agent works 9 am to 5 pm, Monday through Friday. The average number...
A real estate agent works 9 am to 5 pm, Monday through Friday. The average number of sales call this agent gets is 6 per day. Furthermore, assume that the probability of a sales call for this agent is the same for any two days and the sales call in one day are independent of sales call on any other day. Using this information to answer the following questions (40 through 43) pls show work 40. What is the probability...
5. You observed that the time your friend Alice talks on a phone conversation is exponentially...
5. You observed that the time your friend Alice talks on a phone conversation is exponentially distributed with mean 5 minutes. You call her one morning and her line is busy. Assuming that she is in a phone conversation: (a) (8.5 pts) What is the probability that she would finish the conversation in (b) (3 pts) What is the expected additional conservation time before she (c) (6 pts) If the conversation time is uniformly distributed with mean 5 another 5...
Bob owns a car rental company that has a fleet of 10 cars. Each car battery...
Bob owns a car rental company that has a fleet of 10 cars. Each car battery has an Exponentially distributed lifespan with a mean of 2 years. At the beginning of last year (Jan. 1, 2019), Bob replaced all the batteries. a) (5 points) What was the expected number of Batteries that Bob had to replace last year? b) (5 points) What was the probability that Bob had to replace 4 Batteries in 2019? c) (5 points) Bob replaced 3...
3. A customer support center for Bell Computer Company (BMC) receives an average of 2.5 phone...
3. A customer support center for Bell Computer Company (BMC) receives an average of 2.5 phone calls every 5 minutes. Assume that the number of calls received follows Poisson distribution with λ = 2.5 in answering the following questions What is the probability that no calls will arrive during the next five minutes? What is the probability that 5 calls will arrive during the next 5 minutes? What is the probability that at least 3 calls will arrive during the...
(1) Busy car wash Suppose you run a (busy) car wash, and the number of cars that come to the car wash between time 0 and...
(1) Busy car wash Suppose you run a (busy) car wash, and the number of cars that come to the car wash between time 0 and time s > 0 is a Poisson process with rate λ = 1. The number of red cars that come to the car wash between time 0 and time s > 0 is a Poisson process with rate 2. The number of blue cars that come to car wash between time 0 and time...
Conditional Probability Problem 1) A foundry has 3 different production lines and wants to evaluate the...
Conditional Probability Problem
1) A foundry has 3 different production lines and wants to evaluate the performance of each line. The performance of each line is given below Percent of all parts that Percent of all parts that come from each line and Line X Line Y Line Z TOTAL come from each line 44% 36% 20% 100% are defective 3% 4% 1% 19% Parts from all 3 lines merge into a single conveyor to take them to inspection. Consider...
0 points DevoreStat9 3.E 013 A mail-order company business has six telephone lines. Let X denote...
0 points DevoreStat9 3.E 013 A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table 6. -1 My Notes p(x) 0.11 0.15 0.20 0.25 0.19 0.07 0.03 Calculate the probability of each of the following events. (a) fat most three lines are in use) (b) fewer than three lines are in use (c) sat least three lines...
Problem 4: The phone lines to an airline reservation systenm are occupied 50% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline. a) What is the probability that for exactly three calls the lines are occupied? not occupied? all occupied? b) What is the probability that for at least one call the lines are e) What is the expected number of calls in...
For Exercises 3-15 to 3-18, verify that the following functions are probability mass functions, and determine the requested probabilities. 3-15. x 2 x)1/8 2/8 2/8 2/8 18 (a) P(Xs 1) (c) P(-1 X (b) P(X-2) (d) P(X--1 1) or X= 2) 3-28. The data from 250 endothermic reactions involving sodium bicarbonate are summarized as follow Final Temperature Conditions 266 K 271 K 274 K Number of Reactions 70 80 100 33. Determine the cumulative distribution function for the random variable...
random probability course
Problem 1: [60 points) A discrete random variable has the following probability mass function 2s+ 1,2,3 Find: (a) P(x <2) (b) P(l s X<3) (c) E(x) (d) Ea/x) Problem 2: [40 points] Calls to an airline reservation system have a probability of 0.7 of connecting successfully (i.e., not obtaining a busy tone). Assume that 8 independent calls are placed to the airline. (a) What is the probability that at least one call will connect successfully? (b) What...
5. You observed that the time your friend Alice talks on a phone conversation is exponentially distributed with mean 5 minutes. You call her one morning and her line is busy. Assuming that she is in a phone conversation: (a) (8.5 pts) What is the probability that she would finish the conversation in (b) (3 pts) What is the expected additional conservation time before she (c) (6 pts) If the conversation time is uniformly distributed with mean 5 another 5...
Bob owns a car rental company that has a fleet of 10 cars. Each car battery has an Exponentially distributed lifespan with a mean of 2 years. At the beginning of last year (Jan. 1, 2019), Bob replaced all the batteries. a) (5 points) What was the expected number of Batteries that Bob had to replace last year? b) (5 points) What was the probability that Bob had to replace 4 Batteries in 2019? c) (5 points) Bob replaced 3...
Conditional Probability Problem
1) A foundry has 3 different production lines and wants to evaluate the performance of each line. The performance of each line is given below Percent of all parts that Percent of all parts that come from each line and Line X Line Y Line Z TOTAL come from each line 44% 36% 20% 100% are defective 3% 4% 1% 19% Parts from all 3 lines merge into a single conveyor to take them to inspection. Consider...
0 points DevoreStat9 3.E 013 A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table 6. -1 My Notes p(x) 0.11 0.15 0.20 0.25 0.19 0.07 0.03 Calculate the probability of each of the following events. (a) fat most three lines are in use) (b) fewer than three lines are in use (c) sat least three lines...
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